Why do theme files sometimes need to be group writeable?

I just moved my Blog to a new host and I am unable to use the Edit Themes feature to edit the theme. I know I could change the file permissions from 644 to something different like 664, but why do I have to do this? With the previous host the theme files were set to 644 and I could edit them just fine.

How does the file permission system correlate to a logged in admin level wordpress user i.e. How does WordPress (the logged in admin user) correlate to the owner of the files (user account on the web server)? Is WordPress considered the owner of the files, a member of the group and how is this controlled. Is something set when WordPress is initially installed that can get messed up when you move the database and files to a new host?